If aˣ = N, then x = logₐ N. Logarithms turn multiplication into addition and powers into multiplication.
1Laws
logₐ (xy) = logₐ x + logₐ y
logₐ (x/y) = logₐ x − logₐ y
logₐ (xⁿ) = n logₐ x
logₐ a = 1, logₐ 1 = 0
Change of base: logₐ x = log x / log a
2Common values
log 2 ≈ 0.3010, log 3 ≈ 0.4771, log 5 = 1 − log 2 ≈ 0.6990
Characteristic of log of a number with n digits before the decimal point = n − 1